4 Answers
4

Most modern computers offer a feature
called "Wake on LAN". This is designed
to allow a network administrator to
turn on a computer remotely, even when
it is turned off, by sending a "magic
packet". This is used, for instance,
to allow backup programs to run at
night.

Here is a Python script that does this
(if your MAC address is01-23-45-67-89-0a:

Wake On LAN requires another computer on the subnet to be awake, or the Router to support WoL. If this was the case, LogMeIn would already offer the 'Wake Up This Computer' option.
–
JBRWilkinsonFeb 12 '11 at 9:58

First, your Mac must support Wake on Wireless. Second, your router must support Wireless Multimedia Extensions (WME), also known as Wi-Fi Multimedia (WMM).

After your enabled WME on your router, you must enable "Wake for network access" on your Mac. Then check the MAC address of your wireless card of your Mac. Put your Mac into sleep. From a second computer log in to your router and with the WOL (Wake on LAN) option wake up your Mac wirelessly by entering the MAC address.